Link capacity sharing for throughput-blocking optimality

ABSTRACT

The invention concerns an efficient strategy for sharing link bandwidth in a mixed rigid-elastic traffic environment, as well as a strategy for sharing bandwidth among elastic traffic flows. The idea according to the invention is to sharing the link bandwidth among rigid and elastic traffic by dividing the link bandwidth into a first common part C COM  for elastic as well as rigid traffic and a second part C ELA  dedicated for elastic traffic. Subsequently, one or more admission control parameters for the elastic traffic are determined in order to restrict the number of elastic traffic flows simultaneously present on the link. In particular, by formulating a call-level model for elastic traffic and determining a maximum number N ELA  of admissible elastic traffic flows based on call-level constraints for the elastic traffic related to throughput and/or blocking, the so-called throughput-to-blocking trade-off for elastic traffic can be fully considered.

CROSS-REFERENCES TO RELATED APPLICATIONS

This Application for Patent claims the benefit of priority from, andhereby incorporates by reference the entire disclosure of, U.S.Provisional Application for Patent Serial No. 60/159,351, filed Oct. 14,1999.

TECHNICAL FIELD OF THE INVENTION

The present invention generally relates to the field of communicationnetworks, and in particular to link capacity sharing and link bandwidthallocation in such networks.

BACKGROUND

Many communication networks of today support so-called elastic trafficsuch as the “best effort” services provided in Internet Protocol (IP)based networks or the Available Bit Rate (ABR) traffic in ATM networks.Elastic traffic is typically established for the transfer of a digitalobject, such as a data file, a Web page or a video clip for localplayback, which can be transmitted at any rate up to the limit imposedby the link capacity. Web browsing on the Internet in particular is agood and representative example of elastic traffic. Here, the“elasticity” of the traffic is apparent as the user-perceived throughput(normally given in transmitted bits or bytes per time unit) whendownloading for example a web page fluctuates in time depending on theoverall system load.

The services delivered by IP based networks and the Internet inparticular are called “best effort”, because the networks generally donot provide any guarantee of the quality of service (QoS) received bythe applications. The IP network only makes a best effort to provide therequested service. For instance, if an application requests the networkto deliver an IP packet from one end-point to another, the networknormally can not say what the delay through the network will be for thatpacket. In fact, the network does not even guarantee tat the packet willbe delivered at all.

Therefore, terminals connected to an IP network have to handle packetlosses and excessive packet delay situations. Such situations occur whenthere are too many applications simultaneously using the networkresources. These congestion situations have a non-zero probability in IPbased networks, because IP networks do not exercise call admissioncontrol (CAC). In other words, IP networks do not restrict the number ofsimultaneously connected users, and consequently if there are too manyusers utilizing the network resources there will be congestion andpacket losses.

However, with the advent of real-time traffic and QoS requirements in EPnetworks, there is a need for exercising call admission control (CAC) inorder to restrict the number of connections simultaneously present inthe network.

An important aspect of call or connection admission control is that newcalls arriving to the network may be rejected service in order toprotect in-progress calls. In general, CAC algorithms such as thosecommonly in use for rigid traffic in conventional ATM networks provide abasic means to control the number of users in the network, therebyensuring that admitted users get the bandwidth necessary to provide theQoS contracted for. Consequently, a CAC algorithm represents a trade-offbetween the blocking probability for new calls and the providedthroughput for in-progress calls. In other words, the more users thatthe CAC algorithm admits into the network (which reduces the blockingprobability) the smaller the provided throughput per-user becomes, sincea greater number of users will share the total bandwidth, and viceversa.

Recent research has indicated that it is meaningful to exercise calladmission control even for elastic traffic, because CAC algorithmsprovide a means to prevent TCP sessions from excessive throughputdegradations.

The issue of applying CAC for elastic connections, and thereby providinga minimum throughput for Transmission Control Protocol (TCP) connectionsin the Internet has been addressed by Massoulie and Roberts inreferences [1-3]. Here, bandwidth is allocated to different usersaccording to some fairness criteria.

It has been recognized by Gibbens and Kelly in references [4-5] thatthere is an intimate relationship between throughput and blockingprobabilities for elastic traffic, and that this trade-off is connectedto the issue of charging.

It has also been shown by Feng et al. in reference [6] that providing aminimum rate guarantee for elastic services is useful, because in thatcase the performance of the TCP protocol can be optimized.

As the Internet evolves from a packet network supporting a single besteffort service class towards an integrated infrastructure for severalservice classes, there is also a growing interest in devising bandwidthsharing strategies, which meet the diverse needs of peak-rate guaranteedservices and elastic services.

Similarly, modern ATM networks need to support different service classessuch as Constant Bit Rate (CBR) and Available Bit Rate (ABR) classes,and it is still an open question how to optimally share the linkcapacity among the different service classes.

In general, the issue of bandwidth sharing, in the context ofdynamically arriving and departing traffic flows and especially whenusers have different throughput and blocking requirements, is known fromthe classical multi-rate circuit switched framework to be an extremelycomplex problem.

SUMMARY OF THE INVENTION

The present invention overcomes these and other drawbacks of the priorart arrangements.

It is a first object of to invention to devise a link capacity/bandwidthsharing strategy that meets the diverse needs of rigid and elasticservices in a mixed rigid-elastic traffic environment.

In particular, it is desirable to treat the issues of bandwidth sharingand blocking probabilities for elastic traffic in a common framework. Inthis respect, it is a second object of the present invention to providea link capacity sharing mechanism that considers thethroughput-to-blocking trade-off for elastic traffic. Specifically, itwould be beneficial to develop and utilize a link capacity sharingalgorithm that optimizes the throughput-to-blocking trade-off.

It is a further object of the invention to provide an appropriatecall-level model of a transmission link carrying elastic traffic and toapply the call-level model for dimensioning the link bandwidth sharingfor throughput-blocking optimality.

These and other objects are met by the invention as defined by theaccompanying patent claims.

The invention concerns an efficient strategy for sharing link bandwidthin a mixed rigid-elastic traffic environment, as well as a strategy forsharing bandwidth among elastic traffic flows.

Briefly, the idea according to the invention is to share link capacityin a network by dividing the link capacity into a first common part forelastic as well as rigid (non-elastic) traffic and a second partdedicated for elastic traffic based on received network traffic inputs.Subsequently, one or more admission control parameters for the elastictraffic are determined based on the division of link capacity as well asreceived network traffic inputs.

The division of link capacity generally serves to share the linkcapacity between rigid and elastic traffic, and in particular to reservea part of the link capacity to elastic traffic. Preferably, a minimumrequired capacity of the common part relating to rigid traffic isdetermined given a maximum allowed blocking probability for the rigidtraffic. In this way, a certain grade of service (GoS) on call level isguaranteed for the rigid traffic on the link.

The admission control parameter(s) determined for elastic trafficgenerally serves to restrict the number of elastic traffic flowssimultaneously present on the link. In particular, by formulating acall-level model for elastic traffic and determining a maximum number ofadmissible elastic traffic flows based on call-level constraints for theelastic traffic related to throughput and/or blocking, thethroughput-to-blocking trade-off is fully considered. In this respect,the invention is capable of optimally allocating link bandwidth amongelastic connections in the sense that blocking probabilities areminimized under throughput constraints, or the other way around, in thesense that the throughput is maximized under blocking constraints. Inhis way, the invention provides maximum link bandwidth utilization,either in terms of minimum blocking under throughput constraints ormaximum throughput under blocking constraints.

Accordingly, an efficient strategy for sharing bandwidth in a mixedrigid-elastic traffic environment is provided. In particular, thebandwidth sharing algorithm guarantees a maximum blocking for rigidtraffic as well as a minimum throughput and/or a maximum blocking forelastic traffic.

An important technical advantage of the invention is its ability to meetthe diverse needs of rigid traffic and elastic traffic.

Another advantage of the invention is the ability to provide predictablequality of service for both the user and the network provider while atthe same time ensuring high network provider revenue.

By considering only the elastic traffic of the overall traffic in amixed rigid-elastic traffic environment, or alternatively by reducingthe common bandwidth part to zero so that the entire link is reservedfor elastic traffic, the overall link capacity sharing mechanism isreduced to We determination of one or more admission control parametersfor elastic traffic. Admission control for requested new elasticconnections can then be exercised based on such admission controlparameter(s). In particular, by minimizing the blocking probabilitieswith respect to the number of admissible elastic connections under giventhroughput constraints for the elastic traffic, excessive blockingprobabilities are avoided, while ensuring a given user throughput.

Another aspect of the invention concerns the application of a call-levelmodel of a link supporting elastic traffic, for dimensioning the linkbandwidth sharing for throughput-blocking optimality in anadmission-control enabled IP network. In particular, an elastic trafficflow is modeled as having a bandwidth that fluctuates between a minimumbandwidth and peak bandwidth during the holding time of the trafficflow. Furthermore, the elastic traffic is associated with at least oneof a minimum accepted throughput and a maximum accepted blockingprobability.

A further aspect of the invention concerns a computational method fordetermining a Maxkov chain steady state distribution that isparticularly advantageous for large state spaces. The Markov chaindescribes the dynamics of a link carrying a number of traffic classesincluding non-adaptive elastic traffic, and the computational methodprovides a good initial approximation of the steady state distributionbased on Markov chain product form calculations.

Other aspects or advantages of the present invention will be appreciatedupon reading of the below description of the embodiments of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention together with further objects and advantages thereof, willbe best understood by reference to the following description takentogether with the accompanying drawings, in which:

FIG. 1 is a schematic diagram of a communication network according to apreferred embodiment of the invention;

FIG. 2 is a schematic flow diagram of the overall link capacity sharingalgorithm applied in a mixed rigid-elastic IP traffic environmentaccording to a preferred embodiment of the invention;

FIG. 3 is a schematic block diagram of pertinent parts of an IP routeraccording to a preferred embodiment of the invention;

FIG. 4 is a Markov chain state space diagram for an illustrativetransmission link system;

FIG. 5 is a graph illustrating the mean and the variance of thethroughput of adaptive elastic flows as a function of their service timefor an illustrative example of a transmission link system;

FIG. 6 is a schematic diagram illustrating the elastic cut-offparameters that fulfill given QoS requirements for an illustrativeexample of a link system; and

FIG. 7 is a schematic flow diagram of the overall link capacity sharingalgorithm for a mixed CBR-ABR traffic environment according to apreferred embodiment of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

Throughout the drawings, the same reference characters will be used forcorresponding or similar elements.

Throughout the disclosure, the terms connection and flow are used moreor less interchangeably for what is traditionally denoted as a call.

System Overview of an Illustrative Communication Network

For a better understanding, a general overview of an illustrativecommunication network according to a preferred embodiment of theinvention will now be made with reference to FIG. 1.

FIG. 1 is a schematic diagram of a communication network according to apreferred embodiment of the invention. The communication network is hereillustrated as an IP based network, but may be in the form of an ATMnetwork or any other type of network or combination of networks capableof supporting elastic traffic. The communication network 10 is based ona number of interconnected IP routers 20 (ATM switches in the case of anATM network) forming the core network. The core network is accessed bydifferent users 30 (computers, servers, etc.) through access points,with a so called user-network interface (UNI) being defined for theinteraction between the IP routers and the user equipment. Typically, aplurality of users are connected to some form of aggregation point, suchas an access router (AR) 40, which acts an intermediate between theend-users and the core network.

Link capacity sharing, also referred to as bandwidth control in thenetwork context, and packet scheduling normally reside on the networkside of the UNI, within the IP routers 20. In particular, the bandwidthcontrol and packet scheduling are preferably implemented at the outputport side of the routers 20. The overall bandwidth control has two mainfunctions. First, the bandwidth control serves to share the bandwidthbetween different traffic classes. Second, the bandwidth control servesto restrict the number of simultaneously active connections within thetraffic classes. The latter function is hereinafter referred to as calladmission control (CAC), and is normally exercised at the input portside of the IP routers 20, where connections are accepted or rejected inaccordance with some CAC algorithm. The overall bandwidth controlalgorithm, including the CAC algorithm, may be for example implementedas hardware, software, firmware or any suitable combination thereof.

The user-network contract (UNC) is typically defined at the UNI. The UNCusually indicates the QoS to which the user is entitled and also thespecification of the traffic, which the user may inject into thenetwork, along with supplementary data. The supplementary data mayinclude, for example, the time of day during which the user has accessto a particular service, etc. For instance, the UNC may specify that nomore than 1% of the user-injected IP packets (or ATM cells) may be lostby the network and that the user may send in 10 Mbits during any onesecond through the UNI.

The CAC part of the bandwidth control algorithm may use the UNCinformation of multiple users to provide a basic means to control thenumber of simultaneously present users in the network, thereby ensuringthat the admitted users receive the bandwidth required to provide thecontracted QoS. The CAC algorithm represents a trade-off betweenblocking probabilities and the provided throughput; the more users thatthe CAC algorithm admits into the network (which reduces the blockingprobability), the smaller the provided throughput per user becomesbecause a greater number of users will share the network bandwidth.

CAC may be realized by means of the classical signaling exchange knownfor example form conventional communication circuit-switched networks.However, if the majority of the elastic flows in the network are short,such as for many TCP flows on the Internet today, the introduction ofclassical sign exchange to perform admission control may result in largeoverheads. Therefore, an on-the-fly decision to accept or discard thefirst packet of a flow as suggested in reference [3] would be morebeneficial. For this reason, a mechanism based for example on theexisting Resource Reservation Protocol (RSVP) is provided for keepingtrack of the identities of currently active flows, and for classifyingpackets according to these identities as and when they arrive. Todetermine whether a flow is new or not, it is sufficient to compare itsidentifier with that of the flows on a special list of active flows. Ifno packet was received for a certain flow within a given time-outperiod, the flow would be removed from the list of active flows.Admission control is preferably realized by determining a maximum numberof admissible flows based on the prevailing traffic situation in thesystem, and setting the size of the list of active flows accordingly. Ifthe list is full, a new flow will be rejected. Otherwise, the flow willbe accepted and entered into the list.

Link Capacity Sharing Algorithm—the IP Network Example

In the following, a link capacity sharing algorithm according to apreferred embodiment will be described with reference to the particularapplication of an IP based network carrying rigid as well as elastictraffic.

First, a proper call-level traffic model needs to be formulated.Unfortunately, the application of the classical multi-rate call-levelmodels for management of elastic traffic, such as best effort traffic inIP networks or ABR traffic in ATM networks, is everything butstraightforward. For example, it is not possible to associate elastictraffic with a constant bandwidth. Instead, the bandwidth occupied byelastic traffic flows fluctuates in time depending on the current loadon the link and the scheduling and rate control algorithms applied inthe network nodes. The notion of blocking, when applied to elastictraffic flows, is not as straightforward as for rigid traffic, becausean arriving elastic flow might get into service even if at the arrivalinstant there is no bandwidth available. Besides, for many services, theactual residency time of an elastic flow depends on the throughputactually received by the elastic flow.

Multi-class Model of a Transmission Link for Mixed Rigid-elastic Traffic

In the following, an example of a feasible Markovian model of atransmission link serving both peak-bandwidth assured (rigid ornon-elastic) and elastic traffic classes is formulated. For simplicityand clarity, only a single rigid traffic class and two elastic trafficclasses are considered. It should be noted that the model as well as theaccompanying link sharing algorithm can be extended to more generalcases, and of course even simpler cases.

The system under consideration comprises a transmission link of capacityC, which by way of example can be regarded as an integer number in somesuitable bandwidth unit, say Mbps. In this example, calls arriving atthe link generally belong to one of the following three traffic classes:

Class 1—Rigid traffic class flows, characterized by their peak bandwidthrequirement b₁, flow arrival rate λ₁ and departure rate μ₁.

Class 2—Adaptive elastic class flows, characterized by their peakbandwidth requirement b₂, minimum bandwidth requirement b₂ ^(mm), flowarrival rate λ₂ and departure rate μ₂. Although the bandwidth occupiedby adaptive elastic flows may fluctuate as a function of the link load,their actual holding time is not influenced by the received throughputthroughout their residency in the system. This is the case for instancewith an adaptive video codec, which, in case of throughput degradationdecreases the quality of tie video images and thereby occupies lessbandwidth.

Class 3—Non-adaptive elastic class flows, characterized by their peakbandwidth requirement b₃, minimum bandwidth requirement b₃ ^(min), flowarrival rate λ₃ and ideal departure rate μ₃. The ideal departure rate isexperienced when the peak bandwidth is available. The real instantaneousdeparture rate is proportional to the bandwidth of the flows.

We denote the actual bandwidth allocated (reserved) to a flow of class-2and class-3 in a given system state with b₂ ^(r) and b₃ ^(r), both ofwhich vary in time as flows arrive and depart. We will also se thequantity r_(min)=b₁ ^(min)/b_(i) (for i=2 or i=3) associated withelastic flows with minimum bandwidth requirements.

One may think of a non-adaptive elastic class flow as one that uponarrival has an associated amount of data to transmit (W) sampled from anexponentially distributed service requirement, with distribution${{G\quad (x)} = {1 - ^{{- \frac{b_{3}}{\mu_{3}}}\quad x}}},$

which in the case when the peak bandwidth b₃ is available during theentire duration of the flow gives rise to an exponentially distributedservice time with mean 1/μ₃. Since the free capacity of the linkfluctuates in time according to the instantaneous number of flows inservice, the bandwidth given to the non-adaptive elastic flows may dropbelow the peak bandwidth requirement, in which case the actual holdingtime of the flow increases.

All three types of flows arrive according to independent Poissonprocesses, and the holding time for the rigid and adaptive flows areexponentially distributed. As we will see, the moments of the holdingtime of the nonadaptive flows can be determined using the theory ofMarkov reward processes. In short, two types of elastic traffic areconsidered. Elastic traffic is associated with both a peak and a minimumbandwidth requirement, and allowed into service only as long as theminimum bandwidth requirement is fulfilled. The two elastic trafficclasses primarily differ in terms of how their residency time depends onthe acquired throughput.

To ensure a given QoS of the different elastic classes (that, ingeneral, differ in their peak and minimum bandwidth, i.e. b₂≠b₃, b₂^(min)≠b₃ ^(min)) we need to establish some policy, which generallygoverns the bandwidth sharing among the different elastic classes. Forthis reason, we define the following general bandwidth sharing rulesbetween the elastic classes. The following presentation concerns onlytwo elastic classes, but it extends naturally to more than two elasticclasses.

If there is enough bandwidth for all flows to get their respective peakbandwidth demands, then class-2 and class-3 flows occupy b₂ and b₃bandwidth units, respectively.

If there is a need for bandwidth compression, i.e. n₁·b₁+n₂·b₂+n₃·b₃>C,then the bandwidth compression of the elastic flows is such that r₂=r₃,where r₂=b₂ ^(r)/b₂ and, r₃=b₃ ^(r)/b₃, as long as the minimum rateconstraint is met for both elastic classes (i.e. b₂ ^(min)/b₂≦r₂≦1 andb₃ ^(min)/b₃≦r₃≦1).

If there is still need for farther bandwidth compression, but either oneof the two elastic classes does not tolerate further bandwidth decrease(i.e. r_(i) is already b_(i) ^(min)/b_(i) for either i=2 or i=3) at thetime of the arrival of a new flow, then the service class whichtolerates further compression decreases equally the bandwidth occupiedby its flows, as long as the minimum bandwidth constraint is kept forthis traffic class.

Three underlying assumptions of the above exemplary model arenoteworthy. First of all, it is assumed that both types of elastic flowsare greedy, in the sense that they always occupy the maximum possiblebandwidth on the link, which is the smaller of their peak bandwidthrequirement (b₂ and b₃, respectively) and the equal share (in the abovesense) of the bandwidth left for elastic flows by the rigid flows (whichwill depend on the link allocation policy used). Second, it is assumedthat all elastic flows in progress share proportionally equally (i.e.the r_(i)'s are equal) the available bandwidth among themselves, i.e.the newly arrived elastic flow and the in-progress elastic flows will besqueezed to the same r_(j) value. This assumption, as we will see,provides a quite “fair” resource sharing among the elastic flows. Tohave different elastic traffic classes with significantly different QoSthis assumption needs to be modified. If a newly arriving flow decreasedthe elastic flow bandwidth below b₂ ^(min) and b₃ ^(min) (i.e. bothelastic classes are compressed to their respective minima), that flow isnot admitted into the system, but it is blocked and lost. Arriving rigidas well as elastic flows are allowed to “compress” the in-serviceelastic flows, as long as the minimum bandwidth constraints are kept. Asa third point, the model assumes that the rate control of the elasticflows in progress is ideal, in the sense that an infinitesimal amount oftime after any system state change (i.e. flow arrival and departure) theelastic traffic sources readjust their current bandwidth on the link.While this is clearly an idealizing assumption, the buffers at the IPpacket layer could be made large enough to absorb the IP packets untilTCP throttles the senders. The fact that the model assumes immediatesource rate increase whenever possible make the forthcoming throughputand blocking calculations conservative rather than optimistic.

It is intuitively clear that the residency time of the non-adaptiveelastic flows in this system depends not only on the amount of data theywant to transmit, but also on the bandwidth they receive during theirholding times, and vice versa, the amount of data transmitted through anadaptive elastic flow depends on the received bandwidth. In order tospecify this relationship we define the following quantities:

θ₂(t) and θ₃(t) defines the instantaneous throughput of adaptive andnon-adaptive flows, respectively, at time t. For example, if there aren₁, n₂ and n₃ rigid, adaptive, and non-adaptive flows, respectively, inthe system at time t, the instantaneous throughputs for adaptive andnon-adaptive flows are min(b₂, (C−n₁b₁−n₃r₃b₃)/n₂) and min(b₃,(C−n₁b₁−n₂r₂b₂)/n₃), respectively. Note that θ₂(t) and θ₃(t) arediscrete random variables for any t≧0.${\overset{\sim}{\theta}}_{t} = {\frac{1}{t}\quad {\int_{0}^{t}{\theta_{2}\quad (\tau)\quad {\tau}}}}$

defines the throughput of an adaptive flow having a holding time equalto t.

{tilde over (θ)}=∫₀ ^(∞){tilde over (θ)}_(τ)dF(τ)=μ₂∫₀ ^(∞){tilde over(θ)}_(τ)e^(−μ) ^(₂) ^(τ)dτ (random variable) defines the throughput ofan adaptive flow, where F(t) is the exponentially distributed holdingtime.

T_(x)=inf{t|∫₀ ^(τ)θ₃(τ)dτ≧x} (random variable) gives the time it takesfor the system to transmit x amount of data through an elasticnon-adaptive flow.

{circumflex over (θ)}=x/T_(x) defines the throughput of an non-adaptiveflow during the transmission of x data units. Note that θ_(x) is acontinuous random variable.

{circumflex over (θ)}∫₀ ^(∞){circumflex over (θ)}_(x)dG(x)=μ₃/b₃∫₀^(∞){circumflex over (θ)}_(x)e^(−xμ) ^(₃) ^(/b) ^(₃) dx (randomvariable) defines the throughput of an non-adaptive flow, where theamount of transmitted data is exponentially distributed with parameterμ₃/b₃.

Although a number of general bandwidth sharing rules have been definedabove, a more specific link capacity sharing policy, especially one thatconsiders the diverse requirements of rigid and elastic traffic, stillneeds to be presented.

Link Capacity Sharing Algorithm

According to the invention, the Partial Overlap (POL) link allocationpolicy, known from reference [7] describing the POL policy forsimulative analysis in the classical multi-rate circuit switchedframework, is adopted and modified for a traffic environment thatincludes elastic traffic. According to the new so called elastic POLpolicy, the link capacity C is divided into two parts, a common partC_(COM) for rigid as well as elastic traffic and a dedicated partC_(ELA), which is reserved for the elastic flows only, such thatC=C_(COM)+C_(ELA).

Furthermore, admission control parameters, one for each elastic trafficclass present in the system, arc introduced into the new elastic POLpolicy. In this particular example, N_(EL2) denotes the admissioncontrol parameter for adaptive elastic flows and N_(EL3) denotes theadmission control parameter for non-adaptive elastic flows. Eachadmission control parameter stands for the maximum number of admissibleflows of the corresponding elastic traffic class. The admission controlparameters are also referred to as cut-off parameters, since as long asthe maximum number of simultaneous elastic flows of a certain class arepresent on the link, new elastic flows will be rejected, a form ofcut-off.

Under the considered elastic POL policy, the number (n₁, n₂, n₃) offlows in progress on the link is subject to the following constraints:

n ₁ ·b ₁ ≦C _(COM)  (1)

N _(EL2) ·b ₂ ^(min) +N _(EL3) ·b ₃ ^(min) ≦C _(ELA)  (2)

n ₂ ≦N _(EL2)  (3)

n ₃ ≦N _(EL3)  (4)

In (1) the elastic flows are protected from rigid flows. In (2-4) themaximum number of elastic flows is limited by three constraints.Expression (2) protects rigid flows from elastic flows, while (3-4)protect the in-progress elastic flows from arriving elastic flows. Thenew elastic POL policy is fully determined by the division of the linkcapacity, specified by C_(COM), and the admission control parametersN_(EL2), N_(EL3). These parameters are referred to as the outputparameters of the system. The performance of the elastic POL policy canbe tuned by the output parameters, and in particular, it has beenrealized that the setting of the output parameters C_(COM), N_(EL2) andN_(EL3), allows for a tuning of the throughput-to-blocking trade-off forthe elastic traffic classes.

With respect to the throughput-to-blocking trade-off for elastictraffic, the invention is generally directed towards the provision of ahigh link bandwidth utilization under one or more call-level constraintsthat are related to at least one of elastic throughput and elasticblocking probability.

According to a preferred embodiment of the invention, the link capacitysharing algorithm aims at setting the output parameters of the elasticPOL policy in such a way as to minimize call blocking probabilities B₂and B₃ for elastic flows, while being able to take into account ablocking probability constraint (GoS) for the rigid flows as well asminimum throughput constraints for the elastic flows. The throughputconstraints for the elastic flows are introduced because it has beenrecognized that there is a minimum acceptable throughput below which theusers gain no actual positive utility.

Therefore, the rigid traffic class is associated with a maximum acceptedcall blocking probability B₁ ^(max), and the elastic adaptive andelastic non-adaptive traffic classes are associated with minimumaccepted throughputs {tilde over (θ)}_(min) and {circumflex over(θ)}_(min), respectively. Preferably, the throughput constraints areformed as constraints on the probability that the user-perceivedthroughput during transfer of certain amount of data drops below a giventhreshold. Such a performance measure is easier for the user to verifythan the traditional fairness criteria discussed in references [1-3].

Although the blocking probabilities for elastic traffic are beingminimized, it is nevertheless normally advisable, although notnecessary, to have a worst-case guarantee of the call blocking forelastic traffic, and associate also the two elastic traffic classes withmaximum allowed block probabilities B₂ ^(max) and B₃ ^(max).

In this case, the traffic input parameters of the system are the set ofarrival rates (λ₁, λ₂, λ₃) and departure rates (μ₁, μ₂, μ₃) obtainedfrom the network, the bandwidths (b₁, b₂, b₃), the minimum elasticbandwidth demands (b₂ ^(min), b₃ ^(min)), the blocking probabilityconstraints (B₁ ^(max) or the whole set of B₁ ^(max), B₂ ^(max) and B₃^(max)) and the elastic throughput constraints ({tilde over (θ)}_(min)and {circumflex over (θ)}_(min)) The departure rate for non-adaptiveclass can be estimated under the assumption that the bandwidth of thenon-adaptive flows equals b₃.

The parameters and performance measures associated with the rigidtraffic class and the two elastic traffic classes are summarized inTable I below.

TABLE I Input parameters System state Maximum Performance Number CallPeak Minimum accepted Minimum measures of flows Class arrival Departurebandwidth bandwidth blocking accepted Through- in the rate raterequirement requirement probability throughout Blocking put system Rigidλ₁ μ₁ b₁ — B₁ ^(max) — B₁ — n₁ Adaptive λ₂ μ₂ b₂ b₂ ^(min) (B₂ ^(max)){tilde over (θ)}_(min) B₂ {tilde over (θ)} n₂ elasic Non- λ₃ μ₃ b₃ b₃^(min) (B₃ ^(max)) {circumflex over (θ)}_(min) B₃ {circumflex over (θ)}n₃ adaptive elastic

The problem of determining the output parameters of the elastic POLpolicy under blocking and throughput constraints is outlined below withreference to FIG. 2, which is a schematic flow diagram of the overalllink capacity sharing algorithm according to a preferred embodiment ofthe invention. In the first step 101, the required input parameters,such as current arrival and departure rates, bandwidth requirements aswell as the constraints imposed on the traffic, are provided. In step102, the GoS (call blocking) requirement for rigid traffic is guaranteedby the proper setting of C_(COM). In particular, we determine theminimum required capacity of C_(COM) for rigid flows that guarantees thereed blocking probability B₁ ^(max):

min{C _(COM) : B ₁ ≦B ₁ ^(max)}  (5)

where B₁ is the blocking probability of rigid flows. For example, thewell-known Erlang-B formula can be used to estimate such a value ofC_(COM) based on arrival and departure rates and peak bandwidthrequirement for the rigid traffic as inputs. In addition, a maximumnumber N_(COM) of admissible rigid flows can be determined based on theErlang-B analysis and used for admission control of the rigid traffic.

Next, we have to determine a maximum number of elastic flows (N_(EL2),N_(EL3)) that can be simultaneously present in the system at the sametime as the required throughput and blocking requirements are fulfilled.It is intuitively clear that if the maximum number N_(EL2) of adaptiveelastic flows is increased, the blocking probability B₂ of adaptiveelastic flows decreases and the throughput decreases as well.Unfortunately, changing N_(EL2) affects both the blocking probability B₃and throughput of non-adaptive elastic flows and vice-versa.

In this particular embodiment, the link capacity sharing algorithm a atminimizing the blocking probabilities of the elastic traffic classesunder throughput-threshold constants. To accomplish this, the inventionproposes an iterative procedure, generally defined by steps 103-107, fortuning the cut-off parameters so that the throughput-thresholdconstraints are just fulfilled, no more and no less. First, in step 103,initial values of the cut-off parameters are estimated. Next, theperformance of the system is analyzed (step 104) with respect to elasticthroughputs. In particular, the throughputs {tilde over (θ)} and{circumflex over (θ)} offered in the system controlled by the initialvalues of the cut-off parameters are analyzed (step 104) and related(step 105) to the throughput-threshold constraints {tilde over(θ)}_(min) and {circumflex over (θ)}_(min). If the offered throughputsare too low, then the cut-off parameters are reduced (step 106),increasing the blocking probabilities and also increasing thethroughputs. On the other hand, if the offered throughputs are higherthan the throughput-thresholds, then the cut-off parameters can beincreased (step 107) so that the blocking probabilities (as well as thethroughputs) are reduced. In this way, by iteratively reputing the steps104, 105 and 106/107, the blocking probabilities can be reduced to aminimum, while still adhering to the throughput constraints. Once theconstraints are fulfilled to a satisfactory degree, the algorithmoutputs (step 108) the parameters C_(COM), (C_(ELA)), (N_(COM)),N_(EL2), N_(EL3) for use in controlling the actual bandwidth sharing ofthe considered transmission link.

Naturally, the steps 101 to 108 are repeated in response to changingtraffic conditions so as to flexibly adapt the bandwidth sharing to theprevailing traffic situation.

In general, the cut-off parameters have to be reduced to fulfill thethroughput constrain. On the other hand, as the aim is to minimize theelastic blocking probabilities, and as it is advisable to have aworst-case guarantee of the blocking probabilities for elastic traffic,the cut-off parameters must at the same time be as high as possible, andat least high enough to fulfill the worst-case blocking constraints.Depending on the model parameters and the given bounds, it may be thecase that all the constraints can not be satisfied at the same time,which means that the link is overloaded with respect to the GoSrequirements.

FIG. 3 is a schematic block diagram of pertinent parts of an IP router(or an ATM switch) in which a link capacity sharing algorithm accordingto the invention is implemented. The IP router 20 is associated with aninput link and an output link. The router 20 has a control unit 21, aCAC unit 22, an output port buffer 23 for rigid traffic, an output portbuffer 24 for elastic traffic, and an output port scheduler 25.

The control unit 21 is preferably, although not necessarily, realized assoftware on a computer system. The software may be written in almost anytype of computer age, such as C, C++, Java or even specializedproprietary languages. In effect, the link capacity algorithm is mappedinto a software program, which when executed on the computer systemproduces a set of output control parameters C_ELA, C_COM, N_ELA, N_COMin response to appropriate traffic input parameters received from thenetwork and the UNCs by conventional means.

The N_ELA, N_COM parameters represents the cut-off parameters for rigidtraffic and elastic traffic, respectively. In the example of FIG. 3,only a single elastic traffic class is considered, and hence only asingle cut-off parameter N_ELA for elastic traffic is produced by thecontrol unit 21. The cut-off parameters are forwarded to the CAC unit22, which accepts or rejects new flows based on the forwarded cut-offparameters. For each requested new flow, the traffic class of the flowis determined so that admission control can be exercised based on therelevant cut-off parameter. IP packets belonging to accepted rigid flows(restricted by N_COM) are forwarded to the output port buffer 23 forsubsequent scheduling by the output port scheduler 25. In the same way,IP packets belonging to accepted elastic flows (restricted by N_ELA) areforwarded to the output port buffer 24.

The C_ELA, C_COM parameters are forwarded from the control unit 21 tothe output port scheduler 25. The output port scheduler 25 representsthe bandwidth of the output link, and the actual bandwidthrepresentation used in the traffic scheduling is determined by dieC_ELA, C_COM parameters. In the output port scheduler 25, the bandwidthof the output link is divided into a common part C_COM, and a dedicatedpart C_ELA reserved for elastic traffic only. In scheduling IP packets,the output port scheduler 25 can use only the common bandwidth partC_COM for IP packets from the output port buffer 23 for rigid flows. ForIP packets from the output port buffer 24 for elastic flows on the otherhand, the scheduler 25 can use both the dedicated bandwidth part C_ELAand the common bandwidth part C_COM. In this way, the output port outputport scheduler 25 decides how many IP packets that can be sent on theoutput link per time unit and traffic class.

Analysis of Throughput and Blocking Probability Measures of ElasticFlows

The throughput constraints used in the evaluation step 105 (FIG. 2) mayfor example be constraints on the average throughput, where the cut-offparameters fulfills the throughput constraints if:

E({tilde over (θ)})≧{tilde over (θ)}_(min) , E({circumflex over(θ)})≧{circumflex over (θ)}_(min)  (6)

where E stands for the expected value. To make a plausibleinterpretation of this type of constraints, let us assume that thedistribution of θ is fairly symmetric around E(θ). In other words, themedian of θ is close to E(θ). In this case, the probability that anelastic flow obtains less bandwidth than θ^(min) is around 0.5.

However, users often prefers more informative throughput constraints,and an alternative constraint may require that the throughput ofadaptive and non-adaptive flows are greater than {tilde over (θ)}_(min)and {circumflex over (θ)}_(min) with predetermined probabilities (1−ε₂)and (1−ε₃), respectively, independent of the associated servicerequirements (x) or holding times (t):

Pr({tilde over (θ)}_(t)≧{tilde over (θ)}_(min))≧(1−ε₂), Pr({circumflexover (θ)}_(x)≧{circumflex over (θ)}_(min))≧(1−ε₃)  (7)

The worst-case constraints on the elastic blocking probabilities cansimply be expressed as:

B ₂ ≦B ₂ ^(max) , B ₃ ≦B ₃ ^(max)  (8)

In order to obtain the elastic throughput measures (step 104) andpossibly also the elastic blocking me s for given values of the cut-offparameters so as to enable evaluation (step 105) against the givenconstraints, the steady state distribution of a Markov chain describingthe dynamics of the mixed rigid-elastic traffic needs to be determined.As implied in connection with the formulation of the multi-class modelabove, the system under investigation can be represented as a ContinuousTime Markov Chain (CTMC), the state of which is uniquely characterizedby the number of flows of the different traffic classes (n₁, n₂, n₃). Itis clear that in order to obtain the perforce measures of the system wehave to determine the CTMC's generator matrix Q and its steady statedistribution P={P_(i)}, where P ^(T)·Q=0 and Σ_(i)P_(i)=1. The notionsof a generator matrix and a steady state distribution of a Markov chainare considered well known to the skilled person. For a generalintroduction to loss networks, Markov theory and the general stochasticknapsack problem, reference is made to [8], and especially pages 1-69thereof. For given values of the parameters C_(COM), N_(EL2), N_(EL3),the set of triples (n₁, n₂, n₃) that satisfies the constraints of theelastic POL policy given by (1-4) constitute the set of feasible statesof the system denoted by S. The cardinality of the state space can bedetermined as: $\begin{matrix}{{\# \quad S} = {\left( {\frac{C_{COM}}{b_{1}} + 1} \right) \cdot \left( {N_{EL2} + 1} \right) \cdot \left( {N_{EL3} + 1} \right)}} & (9)\end{matrix}$

It is easy to realize that the generator matrix Q possesses a nicestructure, because only transitions between “neighboring states” areallowed in the following sense. Let q_(ij) denote the transition ratefrom state i to state j. Then, taking into account the constraints (1-4)on the number of flows in the system defined by the elastic POL policy,the non-zero transition rates between the states are:

q _(i,ik+)=λ_(k) k=1, 2, 3  (10)

q _(i,ik−) =n _(k)·μ_(k) k=1, 2  (11)

 q _(i,i3−) =n ₃ ·r ₃·μ₃  (12)

where i₁₊=(n₁+1, n₂, n₃) when i=(n₁, n₂, n₃); i_(k+) and i_(k−) (k=1, 2,3) are defined similarly. Expression (10) represents the statetransitions due to a call arrival, while (11) and (12) representtransitions due to call departures. The quantity defined in (12) denotesthe total bandwidth of the non-adaptive flows when the system is instate i. The generator matrix Q of the CTMC is constructed based on thetransition rates defined in (10-12).

For illustrative purposes, let us consider a small system with a rigidclass, an adaptive elastic class and a non-adaptive elastic class, wherethe link capacity C=7. For simplicity, assume a division of the linkcapacity such that n₁=1 is kept fixed, i.e. the available bandwidth forelastic flows is 6 bandwidth units. Furthermore, b₁=1, b₂=3 and b₃=2.The elastic flows are characterized by their minimum acceptedbandwidths, which here are set to b₂ ^(min)=1.8 and b₃ ^(min)=0.8.Setting the cut-off parameters to N_(EL2)=2 and N_(EL3)=3, gives rise to12 feasible states as illustrated in the Markov chain state spacediagram of FIG. 4. There are 5 (gray) states where at least one of theelastic flows is compressed below the peak bandwidth specified by b₂ andb₃. The states are identified by the number of active connections (n₁,n₂, n₃). The values below the state identifiers indicate the bandwidthcompression of the adaptive and non-adaptive elastic traffic (r₂, r₃).The state (1, 2, 3) is the only one where the bandwidth compression ofthe adaptive class and the non-adaptive class differs due to differentminimum bandwidth requirements (r₂ ^(min)=0.6, r₃ ^(min)=0.4).

Different numerical solutions can be used to obtain the steady statedistribution of a so-called multidimensional Markov chain. Directmethods such as the Gaussian elimination method compute the solution ina fixed number of operations. However, when considering the size of thestate space for practically interesting cases, i.e. large state spacesin the order of 10⁴ or higher, the computational complexity of thedirect methods is usually unacceptable. Therefore, an iterative method,such as the biconjugate gradient method applied here, is much morefeasible for the steady state analysis. The biconjugate gradient methodis also detailed in reference [9].

The computation time of an iterative method depends on factors such asthe speed of convergence and the complexity of each iteration step. Thecomputation time is also highly dependent on the initial guess. A goodinitial guess will significantly reduce the overall computation time.For this reason, according to the invention, a heuristic direct methodis applied for calculating a fairly close initial guess to be applied inthe iterative method. Some special multidimensional Markov chainsexhibit a so called product form solution, which means that the steadystate probability of state (i,j) can be efficiently determined inproduct form as f(i)·g(j) instead of h(i,j). Unfortunately, due to theoccasional reduction of the bandwidth (and corresponding departure rate)of the non-adaptive elastic flows, the CTMC of the studied system doesnot exhibit the nice properties of reversibility and product formsolution, but the proposed initial guess used for the subsequentiterative numerical procedure is calculated as if the Markov chainexhibited product form. In other words, the initial form of the steadystate distribution of a Markov chain describing a traffic system thatincludes non-adaptive elastic traffic is determined based on Markovchain product form calculations, and applied in an iterative steadystate analysis method.

The fact that only non-adaptive elastic flows disturb the reversibilityis utilized, and the Markov chain that describes the number of rigid andadaptive elastic flows in the system is reversible, and${{p\quad \left( {n_{1},n_{2}} \right)} = {\sum\limits_{i = 0}^{N_{EL3}}\quad {p\quad \left( {n_{1},n_{2},i} \right)}}},{\forall{\left( {n_{1},n_{2}} \right) \in S}}$

is obtained from: $\begin{matrix}{{p^{*}\quad \left( {0,0} \right)} = 1} & (13) \\{{p^{*}\quad \left( {n_{1},n_{2}} \right)} = {{p^{*}\quad {\left( {{n_{1} - 1},n_{2}} \right) \cdot \frac{\lambda_{1}}{n_{1} \cdot \mu_{1}}}} = {p^{*}\quad {\left( {n_{1},{n_{2} - 1}} \right) \cdot \frac{\lambda_{2}}{n_{2} \cdot \mu_{2}}}}}} & (14) \\{{p\quad \left( {n_{1},n_{2}} \right)} = \frac{p^{*}\quad \left( {n_{1},n_{2}} \right)}{\sum\limits_{{({a,b})} \in S}^{\quad}\quad {p^{*}\quad \left( {a,b} \right)}}} & (15)\end{matrix}$

where the p*(n₁,n₂) unnormalized steady state probabilities areauxiliary variables of the iterative method. From the steady statedistribution of the rigid and adaptive flows (p(n₁,n₂)), the overallsteady state behavior (p(n₁,n₂,n₃)) is obtained by fixing the number ofrigid flows (n_(i)=i) and assuming that the obtained Markov chain isreversible, even though this is not the case. This assumption allows usto evaluate an initial guess for the iterative method as follows. Forall possible fixed values of n₁ (n₁=i): $\begin{matrix}{{p^{*}\quad \left( {i,0,0} \right)} = 1} & (16) \\{{p^{*}\quad \left( {i,n_{2},n_{3}} \right)} = \frac{{p^{*}\quad {\left( {i,{n_{2} - 1},n_{3}} \right) \cdot \lambda_{2}}} + {p^{*}\quad {\left( {i,n_{2},{n_{3} - 1}} \right) \cdot \lambda_{3}}}}{{n_{2} \cdot \mu_{2}} + {n_{3} \cdot \mu_{3} \cdot r_{3}}}} & (17) \\{{p\quad \left( {i,n_{1},n_{2}} \right)} = {p^{*}\quad \left( {i,n_{1},n_{2}} \right)\quad \frac{\sum\limits_{a \in S}^{\quad}\quad {p^{*}\quad \left( {i,a} \right)}}{\sum\limits_{{({a,b})} \in S}^{\quad}\quad {p^{*}\quad \left( {i,a,b} \right)}}}} & (18)\end{matrix}$

In other words, we group states with common n₁, n₂ parameters, summingup their probabilities, to obtain a new 2-dimensional Markov chain. Theobtained 2-dimensional Markov chain exhibits product form, and itssteady state distribution is calculated using equations (13-15). Next,we “share” the probability of the state groups among the individualstates that define a state group using equations (16-18).

The steady state distribution of traffic classes other than thenon-adaptive traffic class is calculated as if there was no non-adaptivetraffic in the system, and then state probabilities are calculated underthe assumption of equilibrium between incoming and outgoing traffic ofone of the other traffic classes and the non-adaptive elastic trafficclass. In the present example, the steady state distribution of therigid traffic class and the adaptive elastic traffic class is calculatedas if there was no non-adaptive elastic traffic in the system, and stateprobabilities are determined assuming that the incoming and outgoingadaptive and non-adaptive elastic traffic are in equilibrium. It shouldthough be understood that equations (13-18) can be adapted to a varietyof applications, for example traffic systems with several rigid trafficclasses but only a single elastic traffic class.

It should also be understood that the above procedure for calculating aninitial approximation of a steady state distribution is generallyapplicable to any multi-dimensional Markov chain and can be adapted todifferent applications,

The obtained initial approximation of the steady state distribution isused as a good initial guess for an iterative method, such as thebiconjugate gradient based method, which improves the initial guessstep-by-step to an appropriate accuracy.

Based on the steady state distribution of the CTMC, the call blockingprobabilities can be calculated as: $\begin{matrix}{{B_{k} = {\sum\limits_{{j \in S},{{{ik} +} \notin S}}^{\quad}\quad p_{i}}},{k = 1},2,3} & (19)\end{matrix}$

The calculation of the average throughput of the adaptive andnon-adaptive elastic flows is also quite straightforward once the steadystate distribution of the CTMC is determined: $\begin{matrix}{{E\quad \left( \overset{\sim}{\theta} \right)} = \frac{\sum\limits_{{({n_{1},n_{2},n_{3}})} \in S}^{\quad}\quad {n_{2}\quad p\quad \left( {n_{1},n_{2},n_{3}} \right)\quad b_{2}\quad r_{2}\quad \left( {n_{1},n_{2},n_{3}} \right)}}{\sum\limits_{{({n_{1},n_{2},n_{3}})} \in S}^{\quad}\quad {n_{2}\quad p\quad \left( {n_{1},n_{2},n_{3}} \right)}}} & (20) \\{{E\quad \left( \overset{\sim}{\theta} \right)} = \frac{\sum\limits_{{({n_{1},n_{2},n_{3}})} \in S}^{\quad}\quad {n_{3}\quad p\quad \left( {n_{1},n_{2},n_{3}} \right)\quad b_{3}\quad r_{3}\quad \left( {n_{1},n_{2},n_{3}} \right)}}{\sum\limits_{{({n_{1},n_{2},n_{3}})} \in S}^{\quad}\quad {n_{3}\quad p\quad \left( {n_{1},n_{2},n_{3}} \right)}}} & (21)\end{matrix}$

Thus, the blocking probability constraints in (5) and (8) as well as theaverage throughout constrains in (6) can be evaluated.

Unfortunately, it is much harder to check the throughput thresholdconstraints in (7), since neither the distribution nor the highermoments of {tilde over (θ)}_(t) and {circumflex over (θ)}_(x) can beanalyzed based on the steady state distribution of the above studiedMarkov chain. Hence, a new analysis approach is applied. The throughputthreshold constraint on adaptive elastic flows can be checked based onthe distribution of {tilde over (θ)}_(t) and the throughput thresholdconstraint on non-adaptive elastic flows can be checked based on thedistribution of T_(x), because:

Pr({circumflex over (θ)}_(x)≧{circumflex over (θ)}_(min))=Pr(x/T_(x)≧{circumflex over (θ)}_(min))=Pr(T _(x) ≦x/{circumflex over (θ)}_(min))  (22)

Since it is computationally to hard to evaluate the distribution ofT_(x) and {tilde over (θ)}_(t) for realistic models, but there areeffective numerical methods to obtain their moments, we check thethroughput threshold constraint by applying a moment based distributionestimation method as disclosed in reference [10] and summarized in TableII below. In Table II, μ_(n) denotes the nth moment of the randomvariable X and the formulas present an upper and lower bound on thedistribution of X. Table II is valid for any non-negative randomvariable, i.e. we do not utilize the fact that T_(x) and {tilde over(θ)}_(t) are upper bounded in our system.

TABLE II Pr(X ≧ 1) ≦ upper limit Pr(X ≧ 1) ≦ upper limit 1 μ₁ 0 2$\frac{\mu_{2} - \mu_{1}^{2}}{\mu_{2} - {2\mu_{1}} + 1},\left( {\mu_{1} \leq 1} \right)$

$\frac{\left( {\mu_{1} - 1} \right)^{2}}{\mu_{2} - {2\mu_{1}} + 1},\left( {\mu_{1} \geq 1} \right)$

3 $\begin{matrix}{\frac{{\mu_{3}\mu_{1}} - \mu_{2}^{2} + {\mu_{2}\mu_{1}} - \mu_{1}^{2}}{\mu_{3} - \mu_{2}},} \\\left( {\frac{\mu_{2} - \mu_{3}}{\mu_{1} - \mu_{2}} \geq 1} \right) \\{\frac{{\mu_{3}\mu_{1}} - \mu_{2}^{2}}{\mu_{3} - {2\mu_{2}} + \mu_{1}},} \\\left( {\frac{\mu_{2} - \mu_{3}}{\mu_{1} - \mu_{2}} < 1} \right)\end{matrix}$

$\begin{matrix}{\frac{\left( {\mu_{2} - \mu_{1}} \right)^{3}}{\left( {\mu_{3} - {2\mu_{2}} + \mu_{1}} \right)\left( {\mu_{3} - \mu_{2}} \right)},} \\\left( {\frac{\mu_{2} - \mu_{3}}{\mu_{1} - \mu_{2}} \geq 1} \right)\end{matrix}$

The method to evaluate the moments of T_(x) and {tilde over (θ)}_(t) isbased on a tagging an elastic flow arriving to the system, and carefullyexam the possible transitions from the instance this tagged flow entersthe system until it leaves the system. The system behavior during theservice of the tagged flow can be described by a slightly modifiedMarkov chain. To analyze {tilde over (θ)}_(t) a tagged adaptive elasticflow is considered, while to analyze T_(x) a tagged non-adaptive elasticflow is considered. The modified system used to evaluate {tilde over(θ)}_(t) (or T_(x)) has the following properties:

Since it is assumed that at least the tagged elastic flow is present inthe system we exclude states where n₂=0 (or n₃=0).

With each state of the state space there is an associated entranceprobability, which is the probability of the event that the modifiedCTMC starts from that state. When the tagged elastic flow finds thesystem in state (n₁,n₂,n₃) it will bring the system into state(n₁,n₂+1,n₃) (or state (n₁,n₂,n₃−1)) unless the state (n₁,n₂,n₃) happensto be a blocking state of the tagged flow.

Let {Z(t), t≧0} be the modified CTMC assuming the tagged elastic flownever leaves the system over the finite state space F with generator B.F can be defined as:

0≦n ₁ ·b ₁ ≦C _(COM)  (23)

1 (or 0)≦n ₂ ≦N _(EL2)  (24)

0 (or 1)≦n ₃ ≦N _(EL3)  (25)

Indeed, F=S\S₀ where S₀ is the states in S where n₂=0 (or n₃=0). Thestate transition rates in B are closely related to the appropriate ratesin Q.

b _(i,ik+)=λ_(k) k=1, 2, 3  (26)

b _(i,i1−) =n _(i)·μ₁  (27)

b _(i,i2−)=(n ₂−1)·μ₂ (or n ₂·μ₂)  (28)

b _(i,i3−) =n ₃ ·r ₃·μ₃ (or (n ₃−1)·r ₃·μ₃)  (29)

The initial probability of the modified Markov chain p⁺(n₁,n₂,n₃) isobtained by considering the system state immediately after the taggedflow joins the system in steady state. This means that the probabilitythat the system is in state (n₁,n₂,n₃) after the tagged flow's arrivalis proportional to the steady state probability of state (n₁,n₂−1,n₃)(or (n₁,n₂,n₃−1)). Consequently: $\begin{matrix}{{p^{2 +}\quad \left( {n_{1},n_{2},n_{3}} \right)} = \frac{p\quad \left( {n_{1},{n_{2} - 1},n_{3}} \right)}{\sum\limits_{i \in F}^{\quad}\quad {p\quad \left( {n_{1},n_{2},n_{3}} \right)}}} & (30) \\{{p^{3 +}\quad \left( {n_{1},n_{2},n_{3}} \right)} = \frac{p\quad \left( {n_{1},n_{2},{n_{3} - 1}} \right)}{\sum\limits_{i \in F}^{\quad}\quad {p\quad \left( {n_{1},n_{2},n_{3}} \right)}}} & (31)\end{matrix}$

To obtain the moments of {tilde over (θ)}_(t), Markov Reward model isdefined over {Z(t), t≧0} in accordance with reference [11]. {tilde over(θ)}_(t) is a random variable which depends on the random arrival anddeparture of the rigid, adaptive and non-adaptive elastic flows asdescribed by B. The reward rate associated we the states of the modifiedMarkov chain represents the bandwidth of the tagged adaptive elasticflows in that state. Let t_(i) be the reward rate (the bandwidth of thetagged adaptive elastic flow) in state i and T the diagonal matrixcomposed of the t_(i) entries. t₁=r₂(i)·b₂, where r₂(i) is the bandwidthcompression in state i. In this way, the dynamics of the number of flowsin the system during the service of the tagged flow is described by theModified Markov chain, and the instantaneous bandwidth of the taggedflow is described by the instantaneous reward rate. If there are moreflows in the system, the bandwidth of the tagged flow decreases towardsb₂ ^(min) and if there are less flows, it increases towards b₂. Thegenerator matrix B and the reward matrix T define the Markov Rewardmodel that accumulates t·{tilde over (θ)}_(t) amounts of reward in theinterval (0, t). This means that the reward accumulated in the interval(0, t) represents the amount of data transmitted through the tagged flowin this interval, and {tilde over (θ)}_(t) is the amount of transmitteddata/t.

T_(x) is the random amount of time that it takes to transmit x units ofdata through the tagged flow. By defining a Markov Reward model asabove, the reward accumulated in the interval (0, t) represents therandom amount of data transmitted through the tagged flow, and henceT_(x) is the time it takes to accumulate x amounts of reward. Thismeasure is commonly referred to as completion time.

Having the initial probability distribution p²⁺(n₁,n₂,n₃), andp³⁺(n₁,n₂,n₃), the generator matrix B and the reward matrix T, thenumerical analysis method proposed in reference [11] is applied toevaluate the moments of {tilde over (θ)}_(t) and T_(x). This numericalmethod is applicable for Markov Reward models with large state spaces(⁻10⁶ states).

Numerical Examples of the Application of the Link Capacity SharingAlgorithm

By way of example, consider a transmission link of capacity C=100 Mbpsand supporting tree different service classes: rigid, adaptive elasticand non-adaptive elastic service classes. The parameters, given asnetwork traffic inputs and determined by the link sharing algorithm, ofthis system are as follows:

C_(COM)=20 Mbps, C_(ELA)=80 Mbps;

b₁=1 Mbps, b₁=5 Mbps, b₃=3 Mbps;

λ₁=λ₃=12 1/min;

μ₁=μ₂=μ₃=1 1/min;

r₂ ^(min)=0.05, r₃ ^(min)=0.001;

N_(COM)=20, N_(EL2)=20, N_(EL3)=20.

The effect of the arrival rate λ₂ of the adaptive elastic flows on thecorresponding blocking probability for a number of values of minimumaccepted throughput is demonstrated in Table III below.

TABLE III Pr({tilde over (θ)}_(t) ≧ {tilde over (θ)}_(min)) ≧ (1-ε₂) λ₂= 12 λ₂ = 14 λ₂ = 16 {tilde over (θ)}_(min) = 2.6 89.4% 83.6% 77.7%   384.2% 75.1% 65.5% 3.4 74.4% 62.0% 50.8% 3.8 64.3% 47.8% 34.9% 4.2 42.5%23.4% 10.5% 4.6 4.8% 0.14% —

As the minimum accepted throughput {tilde over (θ)}_(min) for theadaptive elastic traffic is assigned higher and higher values, theprobability that an adaptive elastic flow obtains this throughputdecreases. The increase of the arrival rate of the adaptive elasticflows results in more adaptive elastic flows in the system, and hencethe throughput decreases together with the probability that the adaptiveelastic flows obtain the required bandwidth.

The effect of the arrival rate λ₃ of the non-adaptive elastic flows onthe corresponding blocking probability for a number of values of minimumaccepted throughput is demonstrated in Table IV below. In this case, thesystem parameters are:

C=250 Mbps;

C_(COM)=50 Mbps, C_(ELA)=200 Mbps;

b₁=1 Mbps, b₂=3 Mbps, b₃=5 Mbps;

λ₁=40 1/min, λ=25 1/min;

μ₁=μ₂=μ₃=1 1/min;

r₂ ^(min)=0.4, r₃ ^(min)=0.05;

N_(COM)=50, N_(EL2)=120, N_(EL3)=180.

Note that in this case the modified Markov chain describing the systembehavior during the service of a tagged non-adaptive elastic flow has1,116,951 states and 6,627,100 transitions.

TABLE IV Pr({tilde over (θ)}_(x) ≧ {circumflex over (θ)}_(min)) ≧ (1-ε₂)λ₃ = 20 λ₃ = 25 λ₃ = 30 {circumflex over (θ)}_(min) = 2.5 99.98% 99.6%88.1% 3.33 99.8% 94.36% 32.5% 4.0  97.4% 68.1% 13.8% 4.34 91.5% 59.8% —4.54 89.6% 52.3% — 4.76 86.0% 30.9% —

In similarity to the effects demonstrated in Table III, as the minimumaccepted throughput for the non-adaptive elastic traffic is assignedhigher and higher values, the probability that a non-adaptive elasticflow obtains this throughput decreases. Also, the increase of thearrival rate results in a decreasing probability that the non-adaptiveelastic flows obtain the required bandwidth.

To get an impression of the relation of average throughput andthroughput threshold constraints reference is made to FIG. 5, whichillustrates the mean and the variance of the throughput of adaptiveelastic flows as a function of their service time. The graph of FIG. 5relates to the system considered for Table III, with λ₂=14. The meanthroughput is shown by a solid line, whereas the variance is shown by adashed line. It can thus be seen that for “short” (with respect toservice time) connections, the variance of the throughput is quitesignificant, and consequently, the average throughput and the throughputthreshold constraints have significantly different meaning. For “long”connections, the variance of the throughput almost vanishes, and themean throughput provides a meaningful description of the bandwidthavailable for adaptive elastic flows. Note that {tilde over (θ)}_(t)tends to approach a deterministic value, the steady state throughput, ast goes to infinity.

Finally, we study an example of how to select N_(EL2) and N_(EL3) toprovide the required QoS parameters. Assume that after the division ofthe link capacity and the dimensioning of the rigid class, the systemsparameters have the following values:

C=100 Mbps;

C_(COM)=20 Mbps, C_(ELA)=80 Mbps;

b₁=1 Mbps, b₂=5 Mbps, b₃=3 Mbps;

λ₁=12 1/min, λ₂=12 1/min, λ₃=12 1/min;

μ₁=μ₂=μ₃=1 s (here expressed as mean holding time);

b₃ ^(min)=0.1 Mbps;

The parameters N_(EL2) and N_(EL3) have to be such that the elasticblocking probabilities are less than 1% (B₂<0.01, B₃<0.01) and theaverage throughput parameters fulfill E({tilde over (θ)})≧4.05 andE({circumflex over (θ)})≧2.35.

The set of N_(EL2) and N_(EL3) parameters that fulfill the QoSrequirements are depicted in the gray area of FIG. 6. The blockingprobability limit of the adaptive elastic class is a vertical line dueto the independence on the load of the non-adaptive elastic class. Theblocking probability limit of the non-adaptive elastic class is ahorizontal line. With the considered low level of overall load, theaverage elastic throughputs are hardly sensitive to the N_(EL2) andN_(EL3) parameters after a given limit. In this example, the tighter ofthe two bandwidth limits that determines the acceptable N_(EL2) andN_(EL3) values, is the E({tilde over (θ)})≧4.05 bound.

Inversion of the Optimization Task

The new elastic POL policy allows for a natural inversion of theoptimization task so that instead of minimizing blocking probabilitiesfor elastic traffic under throughput constraints, the elasticthroughputs are maximized under blocking probability constraints. Insimilarity to the link capacity sharing method illustrated in the flowdiagram of FIG. 2, traffic input parameters are received (similar tostep 101), the common link capacity part C_(COM) is determined (similarto step 102) and initial values of the cut-off parameters are selected(similar to step 103). Next, the performance of the system is analyzed(similar to step 104), but now primarily with respect to elasticblocking probabilities. In particular, the elastic blockingprobabilities in the system are analyzed and related (similar to step105) to the blocking probability constraints. If the blockingprobabilities are too high, then the cut-off parameters are increased,reducing the blocking probabilities and also reducing the throughputs.On the other hand, if the blocking probabilities are lower than theblocking constraints, then the cut-off parameters can be reduced so thatthe blocking probabilities as well as the throughputs are increased. Inthis way, by way of iteration, the throughputs can be increased to amaximum, while still adhering to the blocking constraints for elasticflows. As the aim now is to maximize the elastic throughputs, and as itmight be advisable to have a worst-case guarantee for the through ofelastic traffic, the cut-off parameters must be as low as possible, andat least low enough to fulfill the worst-case throughput constraints,while still fulfill the blocking probability constraints imposed on theelastic traffic.

Naturally, the link capacity sharing algorithm, irrespective of whetherit is adapted for minimizing elastic blocking or for maximizing elasticthroughput, is also applicable to elastic traffic only. For example, inthe absence of rigid traffic, C_(COM) is reduced to zero, and theoverall link capacity sharing algorithm is reduced to the mathematicalformulas for determining the cut-off parameters underthroughput/blocking constraints. Furthermore, in the case of a singleelastic traffic class, only a single cut-off parameter needs to bedetermined according to the above iterative link sharing algorithm.

Link Capacity Sharing Algorithm—the ATM Network Example

Although, the link capacity sharing algorithm has been described abovewith reference to an IP network carrying a single rigid traffic classand two different elastic traffic classes, it should be understood thatthe invention is not limited thereto, and that the algorithm isapplicable to other types of networks and other traffic classes. Infact, an example of the elastic POL algorithm applied in an ATM networkcarrying narrow-band CBR (Constant Bit Rate) traffic and wide-band CBRtraffic, as well as ABR (Available Bit Rate) traffic will be outlinedbelow.

In this example, calls arriving at a transmission link generally belongto one of the following three traffic classes:

Class 1—Narrow-band CBR calls, characterized by their peak bandwidthrequirement b₁, call arrival rate λ₁ and departure rate μ₁.

Class 2—Wide-band CBR calls, characterized by their peak bandwidthrequirement b₂, call arrival rate λ₂ and departure rate μ₂.

Class 3—ABR calls, characterized by their peak bandwidth requirement b₃,minimum bandwidth requirement b₃ ^(min), call arrival rate λ₃ and idealdeparture rate μ₃. The ideal departure rate is experienced when the peakbandwidth is available during the entire duration of the call.

It should be noted that the CBR classes can be likened by the rigidtraffic class of the above IP network example, and that the ABR classcan be likened by the non-adaptive elastic traffic class described abovein connection with the IP network example. In this respect, theassumptions in the model formulated in the IP network example areequally applicable in the present example.

The elastic POL policy described above is applied to the mixed CBR-ABRtraffic environment in the ATM network considered. This means that thelink capacity C is divided into two parts, a common part C_(COM) for CBRcalls as well as ABR calls, and a dedicated part C_(ABR), which isreserved for the ABR calls, such that C=C_(COM)+C_(ABR). An admissioncontrol parameter N_(ABR), also referred to as a cut-off parameter, isintroduced for the ABR calls. Under the elastic POL policy, the numbern₁, n₂ and n₃ of narrow-band CBR, wide-band CBR and ABR calls,respectively, in progress on the link is subject to the followingconstraints:

n ₁ ·b ₁ +n ₂ ·b ₂ ≦C _(COM)  (32)

N _(ABR) ·b ₃ ^(min) ≦C _(ABR)  (33)

n ₃ ≦N _(ABR)  (34)

In (1) the ABR calls are protected from CBR calls. In (2-3) the maximumnumber of ABR calls is limited by two constraints. Expression (2)protects CBR calls form ABR calls, while (3) protects the in-progressABR calls from new ABR calls. In this case, the elastic POL policy isfully determined by the division of the lint capacity, specified byC_(COM), and the admission control parameter N_(ABR). The performance ofthe elastic POL policy is tuned by these parameters.

According to a preferred embodiment of the invention, the link capacitysharing algorithm aims at setting the output parameters C_(COM) andN_(ABR) of the elastic POL policy in such a way as to minimize the callblocking probability for the ABR calls, while being able to take intoaccount blocking probability constraints (GoS) for the different typesof CBR calls and a minimum throughput constraint for the ABR calls.Therefore, each CBR class is associated with a maximum accepted callblocking probability B₁ ^(max) and B₂ ^(max), and the ABR class isassociated with a minimum accepted throughput θ_(min), which can betreated in similarity to the minimum accepted throughput {circumflexover (θ)}_(min) for the non-adaptive elastic traffic of the IP networkexample.

Although the ABR blocking probability is being minimized, it isnevertheless normally advisable, although not necessary, to have aworst-case guarantee of the call blocking probability for ABR calls, andassociate also the ABR class with a maximum allowed blocking probabilityB₃ ^(max).

The parameters and performance measures associated with the CBR classesand the ABR class are summarized in Table V below.

TABLE V Input parameters System state Maximum Performance Number CallPeak Minimum accepted Minimum measures of flows Class arrival Departurebandwidth bandwidth blocking accepted Through- in the rate raterequirement requirement probability throughout Blocking put system N-CBRλ₁ μ₁ b₁ — B₁ ^(max) — B₁ — n₁ W-CBR λ₂ μ₂ b₂ — B₂ ^(max) B₂ — n₂ ABR λ₃μ₃ b₃ b₃ ^(min) (B₃ ^(max)) θ_(min) B₃ θ n₃

The problem of determining the output parameters of the elastic POLpolicy under the above constraints is outlined below with reference toFIG. 7, which is a schematic flow diagram of the overall link capacitysharing algorithm for a mixed CBR-ABR traffic environment according to apreferred embodiment of the invention. In the first step 201, therequired input parameters are provided. In step 202, the GoS (callblocking) requirement for CBR traffic is guaranteed by the propersetting of C_(COM). In particular, we determine the minimum requiredcapacity of C_(COM) for CBR calls that guarantees the required blockingprobabilities B₁ ^(max) and B₂ ^(max):

min{C _(COM) : B ₁ ≦B ₁ ^(max), B₂ ≦B ₂ ^(max)}  (35)

For example, the well-known Erlang-B formula can be used to estimatesuch a value of C_(COM) based on arrival and de e rates and peakbandwidth requirements for the CBR classes as inputs.

Next, we have to determine a maximum number of ABR calls (N_(ABR)) thatcan be simultaneously present in the system at the same time as therequired throughput and blocking requirements are fulfilled.

In this particular embodiment, the link capacity sharing algorithm aimsat minimizing the blocking probability of the ABR calls under a minimumthroughput constraint. To accomplish this, the invention proposes aniterative procedure, generally defined by steps 203-207, for tuning thecut-off parameter so that the throughput-threshold constraint is justfulfilled, generally no more and no less. First, in step 203, an initialvalue of the cut-off parameter is estimated. Next, the performance ofthe system is analyzed (step 204) with respect to the ABR throughput,and related (step 205) to the throughput-threshold constraint. If theABR throughput is too low, then the cut-off parameter is reduced (step206), increasing the blocking probability and also increasing thethroughput. On the other hand, if the ABR throughput is higher than thethroughput-threshold, then the cut-off parameter can be increased (step207) so that the blocking probability (as well as the throughput) isreduced. In this way, by iteratively repeating the steps 204, 205 and206/207, the ABR blocking probability can be reduced to a minimum, whilestill adhering to the throughput constraint.

Preferably, the performance measures, ABR throughput and possibly alsoABR blocking, are analyzed in more or less the same way as describedabove in connection with the IP network example. In short, this meansdetermining the steady state distribution of the Markov chain thatdescribes the dynamics and behavior of the mixed CBR-ABR environment,and calculating blocking and throughput measures based on the determineddistribution. It should though be noted that here thethroughput-threshold constraint, analogous to expression (7), is checkedbased on the transient analysis of the Markov chain that describes themixed CBR-ABR environment using the numerical method proposed inreference [11] and applying the Markov inequality.

It is of course possible to invert the optimization task also for theATM network example, in substantially the same manner as explained abovefor the IP network example.

Numerical Examples of the Application of the Link Capacity SharingAlgorithm

By way of example, consider an ATM transmission link of capacity C=155Mbps and supporting three different service classes; two CBR classes andan ABR class, as described above. The input parameters of this ATMtransmission link system are:

b₁ (n-CBR)=3 Mbps, b₂ (w-CBR)=6 Mbps, b₃ (ABR)=10 Mb;ps

λ₁=6 1/s, λ₂=3 1/s, λ₃=12 1/s;

μ₁=μ₂=μ₃=1 1/min;

r₂ ^(min)=0.05, r₃ ^(min)=0.001;

N_(COM)=50.

Furthermore, it is required that the blocking probabilities of thenarrow-band and wide-band CBR calls are less than B₁ ^(max)=2% and B₂^(max)=4%, respectively. It thus follows that the minimal bandwidth forC_(COM) necessary to provide these blocking probabilities is 60 Mbps,which leaves C_(ABR)=95 Mbps for the ABR calls.

To examine the trade-off between throughput and blocking probability forthe ABR traffic, reference is made to Table VI below, which illustratesthe average throughput E(θ) and the blocking probability B₃ for the ABRtraffic class for different values of N_(ABR).

TABLE VI N_(ABR) 10 20 40 60 80 100 150 B₃ 0.310 0.0811 0.0320 0.02120.00141 0.00112 0.000461 E(θ) 9.99 7.9 4.83 3.45 2.69 2.2 1.52

From Table VI, the trade-off between throughput and blocking isapparent; high-blocking=high throughput, and low blocking=lowthroughput. In the elastic POL policy according to the invention, thistrade-off is conveniently controlled by means of the N_(ABR) cut-offparameter as can be seen from Table VI. For instance, when constraintθ^(min) on the average throughput is set to 2.2 Mbps, the maximum number(N_(ABR)) of simultaneously active ABR calls is limited to 100.

In simulations, it has been observed that the elastic POL policy issuperior to the well-known Complete Partitioning (CP) policy under allloads, both in terms of blocking probabilities and ABR throughput. Thisis partly due to the fact that the POL policy allows ABR calls to makeuse of any bandwidth of the C_(COM) part currently not used by CBRcalls.

Finally, to examine the impact of the C_(COM) parameter on the blockingprobabilities and the average throughput of ABR traffic, reference ismade to Table VII below.

TABLE VII C_(COM) 69 66 63 60 57 54 B₁ 0.00498 0.00770 0.0116 0.01710.0244 0.0342 B₂ 0.0126 0.0192 0.0284 0.0411 0.0578 0.0794 B₃ 0.01490.0141 0.0129 0.0115 0.00973 0.00773 E(θ) 2.04 2.08 2.13 2.20 2.31 2.46

The C_(COM) parameter offers a way of controlling the trade-off betweenthe CBR blocking probabilities on one hand, and the ABR blockingprobability and throughput on the other hand. Prom Table VII, it can beseen that both the ABR throughput (increasing) and the ABR blocking(decreasing) are improved at the expense of degrading CBR blockingprobabilities.

It is important to understand that the preceding description is intendedto serve as a framework for an understanding of the invention. Theembodiments described above are merely given as examples, and it shouldbe understood that the present invention is not limited thereto. Furthermodifications, changes and improvements which retain the basicunderlying principles disclosed and claimed herein are within the scopeand spirit of the invention.

REFERENCES

[1] L. Massoulie, J. Roberts, “Bandwidth Sharing: Objectives andAlgorithms”, IEEE Infocom '99, pp. 1395-1403, March 1999.

[2] L. Massoulie, J. Roberts, “Bandwidth Sharing and Admission Controlfor Elastic Traffic”, ITC Specialist Seminar, Yokohama, October 1998.

[3] L. Massoulie, J. Roberts, “Arguments in Favour of Admission Controlfor TCP Plows”, 16^(th) International Teletraffic Congress, Edinburgh,UK, June, 1999.

[4] R. J. Gibbens and F. P. Kelly, “Distributed Connection AcceptanceControl for a Connectionless Network”, 16^(th) International TeletrafficCongress, Edinburgh, UK, June, 1999.

[5] F. P. Kelly, “Charging and Rate Control for Elastic Traffic”,European Transaction on Telecommunications, pp. 33-37, Vol. 8, 1997.

[6] Wu-chang Feng, Dilip D. Kandlur, Debanjan Saha and Kang. G. Shin,“Understanding and Improving TCP Performance Over Networks with MinimumRate Guarantees”, IEEE/ACM Transactions on Networking, pp. 173-187, Vol.7, No. 2, April 1999.

[7] E. D. Sykas, K. M. Vlakos, I. S. Venieris, E. N. Protonotarios,“Simulative Analysis of Optimal Resource Allocation and Routing inIBCN's”, IEEE J-SAC, Vol. 9, No. 3, 1991.

[8] Keith W. Ross, “Multi-service Loss Models for BroadbandTelecommunication Networks”, Springer-Verlag, 1995, ISBN 3-540-19918-7.

[9] W. J. Stewart, “Introduction to the Numerical Solution of MarkovChains”, pp. 220-221, Princeton University Press, Princeton, N.J., ISBN0-691-03699-3, 1994.

[10] M. Frontini, A. Tagliani, “Entropy-convergence in Stieltjes andHamburger moment problem”, Appl. Math. and Comp., 88, pp. 39-51, 1997.

[11] M. Telek and S. Rácz, “Numerical analysis of large Markov rewardmodels”, Performance Evaluation, 36&37:95-114, August 1999.

[12] A. Smith, J. Adams, G. Tagg, “Available Bit Rate—A New Service forATM”, Computer Networks and ISDN Systems, 28, pp. 635-640, 1996.

What is claimed is:
 1. A method for sharing link capacity in a networkcomprising the steps of: receiving network traffic input parameters;dividing said link capacity into a first part common to elastic trafficand non-elastic traffic and a second part dedicated for elastic traffic,based on at least part of said network traffic input parameters; anddetermining at least one admission control parameter for said elastictraffic based on said division of link capacity and at least part ofsaid network traffic input parameters.
 2. The method according to claim1, further comprising the step of exercising admission control forelastic traffic flows based on said determined admission controlparameter(s).
 3. The method according to claim 1, wherein said dividingstep includes the step of determining a minimum required capacity ofsaid common part relating to non-elastic traffic given at least onemaximum allowed blocking probability for said non-elastic traffic. 4.The method according to claim 1, wherein said step of determining atleast one admission control parameter comprises the step of determininga maximum number of admissible elastic traffic flows based on at leastone call-level constraint imposed on said elastic traffic.
 5. The methodaccording to claim 4, wherein said step of determining a maximum numberof admissible elastic traffic flows is based on a call-level model forelastic traffic, and said call-level constraint(s) is related to atleast one of throughput and blocking probability of said elastictraffic.
 6. The method according to claim 5, wherein said step ofdetermining a maximum number of admissible elastic traffic flowscomprises the steps of: determining an initial value of the number ofadmissible elastic traffic flows on a link in said network; iterativelyperforming the steps of: i) evaluating said throughput/blockingconstraint(s) imposed on said elastic traffic based on theinitial/current value of the number of admissible elastic traffic flows;and ii) adjusting said number of admissible elastic traffic flows basedon said evaluation; and terminating said iteration process andextracting said maximum number of admissible elastic traffic flows whensaid constraint(s) is/are met.
 7. The method according to claim 6,wherein said step of adjusting said number of admissible elastic trafficflows based on said evaluation comprises the steps of: reducing saidnumber of admissible elastic traffic flows if a value related to thethroughput of said elastic traffic flows is lower than a predeterminedthreshold given by said throughput/blocking constraint(s); andincreasing said number of admissible elastic traffic flows if saidthroughput related value is higher than said threshold.
 8. The methodaccording to claim 4, wherein said step of determining said maximumnumber of admissible elastic connections is based on minimizing theblocking probability of requested elastic traffic connections withrespect to the number of admissible elastic traffic connections under atleast one throughput-threshold constraint for in-progress elastictraffic connections.
 9. The method according to claim 8, wherein saidminimization of the blocking probability of elastic traffic under atleast one throughput-threshold constraint is performed also under atleast one given constraint on maximum allowed blocking probability forelastic traffic.
 10. The method according to claim 4, wherein said stepof determining said maximum number of admissible elastic connections isbased on maximizing the elastic traffic throughput with respect to thenumber of admissible elastic traffic connections under at least oneblocking probability constraint for requested elastic trafficconnections.
 11. The method according to claim 1, wherein said elastictraffic comprises a number of elastic traffic classes, and said step ofdetermining at least one admission control parameter comprises the stepof determining, for each of one said elastic traffic classes, a maximumnumber of admissible elastic traffic flows based on a respectivethroughput/blocking probability constraint imposed on the elastictraffic class.
 12. The method according to claim 1, wherein said networktraffic input parameters include at least said link capacity, at leastone blocking probability constraint for non-elastic traffic, and atleast one throughput/blocking constraint for elastic traffic.
 13. Themethod according to claim 1, wherein said network traffic inputparameters further include arrival and departure rates as well as peakbandwidth requirements for nonelastic and elastic traffic, and a minimumbandwidth requirement for elastic traffic.
 14. The method according toclaim 1, wherein said elastic traffic comprises at least one of thefollowing: adaptive elastic traffic flows of Internet Protocol (IP)networks, non-adaptive elastic traffic flows of IP networks, andAvailable Bit Rate (ABR) flows of ATM networks.
 15. A method forallocating link bandwidth among and within different traffic classes ina network, wherein said traffic classes include at least one elastictraffic class, said method comprising the steps of: partitioning saidlink bandwidth into a first part common to all traffic classes, and asecond part dedicated to connections of said elastic traffic class(es);and allocating said second dedicated part of said link bandwidth toconnections of said elastic traffic class(es) based on link bandwidthutilization under at least one throughput/blocking constraint imposed onthe connections of said elastic traffic class(es).
 16. The methodaccording to claim 15, further comprising the step of allocating aminimum required bandwidth of said common part to connections ofnon-elastic traffic classes given at least one maximum allowed blockingprobability for said non-elastic traffic connections.
 17. The methodaccording to claim 15, further comprising the step of determining amaximum number of admissible elastic traffic connections on the linkbased on said throughput/blocking constraint(s), wherein said step ofallocating bandwidth to connections of said elastic traffic class(es) isbased on said maximum number of admissible elastic traffic connections.18. The method according to claim 17, wherein said step of determining amaximum number of admissible elastic traffic connections is based onminimizing the blocking probability of elastic traffic connections withrespect to the number of admissible elastic traffic connections under atleast one throughput-threshold constraint for in-progress elastictraffic connections.
 19. The method according to claim 17, wherein saidstep of determining a maximum number of admissible elastic trafficconnections is based on maximizing the throughput of in-progress elastictraffic connections with respect to the number of admissible elastictraffic connections under at least one blocking probability constraintfor requested elastic traffic connections.
 20. The method according toclaim 17, wherein said step of determining a maximum number ofadmissible elastic traffic connections comprises the steps of:determining an initial value of the number of admissible elastic trafficconnections on said link; iteratively performing the steps of: i)determining throughput/blocking-probability measures based on theinitial/current of the number of admissible elastic traffic connectionson said link; ii) evaluating said throughput/blocking constraint(s)imposed on said elastic traffic based on the determinedthroughput/blocking measures; and iii) adjusting said number ofadmissible elastic traffic connections based on said evaluation; andterminating said iteration process and extracting said maximum number ofadmissible elastic traffic connections when substantially meeting saidconstraint(s).
 21. An electronically implemented method for sharing linkcapacity among elastic traffic connections in a network, comprising thesteps of: receiving network traffic input parameters; determining amaximum number of admissible elastic traffic connections on said linkbased on said network traffic input parameters, based on maximizing thethroughput of in-progress elastic traffic connections with respect tothe number of admissible elastic traffic connections under at least oneblocking probability constraint for requested elastic trafficconnections, said input parameters including at least onethroughput/blocking constraint imposed on said elastic traffic;receiving requests for elastic traffic connections on a link in saidnetwork; and exercising admission control for said requested elastictraffic connections based on said determined maximum number ofadmissible elastic traffic connections.
 22. The method according toclaim 21, wherein said step of determining a maximum number ofadmissible elastic connections is based on minimizing the blockingprobability of requested elastic traffic connections with respect to thenumber of admissible elastic traffic connections under at least onethroughput-threshold constraint for in-progress elastic trafficconnections.
 23. The method according to claim 21, wherein said step ofdetermining a maximum number of admissible elastic traffic connectionscomprises the steps of: initially determining a number of admissibleelastic traffic connections on said link; iteratively performing thesteps of: i) evaluating said throughput/blocking constraint(s) imposedon said elastic traffic based on the current number of admissibleelastic traffic connections on said link; and ii) adjusting said numberof admissible elastic traffic connections based on said evaluation; andterminating said iteration process and extracting said maximum number ofadmissible elastic traffic connections when said constraint(s) is/aremet.
 24. The method according to claim 23, wherein said step ofadjusting said number of admissible elastic traffic connections based onsaid evaluation comprises the step of selectively, in dependence on therelation between a throughput/blocking measure and saidthroughput/blocking constraint(s), reducing or increasing said number ofadmissible elastic traffic connections.
 25. The method according toclaim 21, wherein: said elastic traffic comprises a number of elastictraffic classes; said step of determining a maximum number of admissibleelastic traffic connections on said link comprises the step ofdetermining, for each of said elastic traffic classes, a traffic-classspecific maximum number of admissible elastic traffic flows based on arespective throughput/blocking probability constraint imposed on theelastic traffic class in question; and said method further comprises thesteps of: determining the associated traffic class for each of saidrequested connections; and controlling admission of each requestedconnection based on the corresponding traffic-class specific maximumnumber of admissible elastic connections.
 26. The method according toclaim 21, wherein said network traffic input parameters include linkcapacity, arrival and departure rates, peak bandwidth and minimumbandwidth requirements for elastic traffic as well as at least onethroughput/blocking constraint imposed on said elastic traffic.
 27. Adevice for sharing link capacity in a network, comprising: means forreceiving network traffic input parameters; means for dividing said linkcapacity into a first part common to elastic traffic and non-elastictraffic and a second part dedicated for elastic traffic, based on atleast part of said network traffic input parameters; and meansdetermining at least one admission control parameter for said elastictraffic based on said division of link capacity and at least part ofsaid network traffic input parameters.
 28. The device according to claim27, further comprising means for exercising admission control forelastic traffic flows based on said determined admission controlparameter(s).
 29. The device according to claim 27, wherein saiddividing means includes means for determining a minimum requiredcapacity of said common part relating to non-elastic traffic given atleast one maximum allowed blocking probability for said non-elastictraffic.
 30. The device according to claim 27, wherein said means fordetermining at least one admission control parameter comprises means fordetermining a maximum number of admissible elastic traffic flows basedon at least one throughput/blocking constraint imposed on said elastictraffic.
 31. The device according to claim 30, wherein said means fordetermining a maximum number of admissible elastic traffic flows isconfigured for: initially determining a number of admissible elastictraffic flows on a link in said network; iteratively evaluating saidthroughput/blocking constraint(s) imposed on said elastic traffic basedon the current number of admissible elastic traffic flows and adjustingsaid number of admissible elastic traffic flows based on saidevaluation; and terminating said iteration process and extracting saidmaximum number of admissible elastic traffic flows when meeting saidconstraint(s).
 32. The device according to claim 30, wherein said meansfor determining a maximum number of admissible elastic traffic flows isconfigured to determine said maximum number based on minimizing theblocking probability of requested elastic traffic connections withrespect to said maximum number of admissible elastic traffic connectionsunder at least one throughput-threshold constraint for in-progresselastic traffic connections.
 33. The device according to claim 30,wherein said means for determining a maximum number of admissibleelastic traffic flows is configured to determine said maximum numberbased on maximizing elastic traffic throughput with respect to saidmaximum number of admissible elastic traffic connections under at leastone blocking probability constraint for elastic traffic.
 34. The deviceaccording to claim 27, wherein said receiving means receives networktraffic input parameters including said link capacity, arrival anddeparture rates and peak bandwidth requirements for non-elastic as wellas elastic traffic, a minimum bandwidth requirement for elastic traffic,at least one blocking probability constraint for non-elastic traffic,and at least one throughput/blocking constraint for elastic traffic. 35.The device according to claim 27, wherein said elastic traffic comprisesat least one of the following, adaptive elastic traffic flows ofInternet Protocol (IP) networks, non-adaptive elastic traffic flows ofIP networks, and available bit rate (ABR) flows of ATM networks.
 36. Anelectronic system for allocating link bandwidth among and withindifferent traffic classes in a network, at least one of said differenttraffic classes being an elastic traffic class, said electronic systemcomprising: a processor configured for: partitioning said link bandwidthinto a first part common to all traffic classes, and a second partdedicated to connections of said elastic traffic class(es); andallocating said second dedicated part of said link bandwidth toconnections of said elastic traffic class(es) based on link bandwidthutilization under at least one throughput/blocking constraint imposed onthe connections of said elastic traffic class(es).
 37. The electronicsystem according to claim 36, wherein said processor is configured forallocating a minimum required bandwidth of said common part toconnections of non-elastic traffic classes given at least one maximumallowed blocking probability for said non-elastic traffic connections.38. The electronic system according to claim 36, wherein said processoris further configured for determining a maximum number of admissibleelastic traffic connections on the link based on saidthroughput/blocking constraint(s), and for allocating bandwidth to saidelastic traffic connections based on said dedicated part of the linkbandwidth as well as said maximum number of admissible elastic trafficconnections.
 39. The electronic system according to claim 38, whereinsaid processor is further configured for determining said maximum numberof admissible elastic connections based on minimizing the blockingprobability of elastic traffic connections with respect to the number ofadmissible elastic traffic connections under at least onethroughput-threshold constraint for in-progress elastic trafficconnections.
 40. The electronic system according to claim 38, whereinsaid processor is further configured for determining said maximum numberof admissible elastic connections based on maximizing the throughput ofelastic traffic connections with respect to the number of admissibleelastic traffic connections under at least one blocking probabilityconstraint for elastic traffic connections.
 41. An electronic system forsharing link capacity among elastic traffic connections in a network,comprising a processor responsive to network traffic input parametersand configured for: determining a maximum number of admissible elastictraffic connections based on at least one throughput/blocking constraintimposed on said elastic traffic, based on minimizing the blockingprobability of requested elastic traffic connections with respect tosaid maximum number of admissible elastic traffic connections under atleast one throughput-threshold constraint for in-progress elastictraffic connections; receiving request for elastic traffic connections;and exercising admission control for said:requested elastic trafficconnections based on said determined maximum number of admissibleelastic traffic flows.
 42. The electronic system according to claim 41,wherein said processor is further configured for determining saidmaximum number of admissible elastic connections based on iterativelyimproving link bandwidth utilization under said throughput/blockingconstraint(s).
 43. The electronic system according to claim 42, whereinsaid processor is further configured for determining said maximum ofadmissible elastic connections based on maximizing elastic traffic,throughput with respect to said maximum number of admissible elastictraffic connections under at least one blocking probability constraintfor elastic traffic.
 44. A method for link bandwidth sharing in anadmission-control enabled IP network, comprising the step of: applying acall-level model of a link carrying a number n, where n is an integerequal to or greater than 1, of elastic traffic classes for dimensioningthe link bandwidth sharing for throughput-blocking optimality, whereinsaid call-level model is defined by: said link having a predeterminedbandwidth capacity C; and for each one of said n elastic trafficclasses, the elastic traffic being modeled as: i) having a peakbandwidth requirement and a minimum bandwidth requirement; ii) occupyingthe maximum possible bandwidth within said peak and minimum bandwidthrequirements; and iii) being associated with at least one of a minimumaccepted throughput and a maximum accepted blocking probability.
 45. Themethod according to claim 44, wherein, for each one of said n trafficclasses, the elastic traffic is further being modeled as: iv) arrivingdynamically according to a Poisson process and being associated with anarrival rate as well as a departure rate; v) sharing proportionallyequally the bandwidth available for the elastic traffic class among theelastic flows; and vi) being associated with a minimum holding time. 46.The method according to claim 44, wherein said n elastic traffic classesinclude a first traffic class for adaptive elastic flows, and a secondtraffic class for non-adaptive elastic flows.
 47. A method fordetermining a steady state distribution of Markov chain describing thedynamics of a network link carrying traffic of a number of trafficclasses including a non-adaptive elastic traffic class, said methodcomprising the steps of: determining a link capacity sharing policy forsaid link; determining a multi-dimensional Markov chain having a set offeasible states for the number of active connections of said trafficclasses according to constraints imposed by said link sharing policy;calculating an initial approximation of the steady state distribution ofsaid Markov chain based on Markov chain product form calculations; anditeratively determining the steady state distribution starting from saidinitial approximation of the steady state distribution.
 48. The methodaccording to claim 47, wherein said step of calculating an initialapproximation of the steady state distribution comprises the steps of:determining the steady state distribution of traffic classes other thansaid non-adaptive traffic class as if there is no non-adaptive elastictraffic in the system; and determining state probabilities assumingequilibrium of the incoming and outgoing traffic of one of said othertraffic classes and said non-adaptive elastic traffic class.
 49. Themethod according to claim 47, wherein said step of iterativelydetermining the steady state distribution is based on a biconjugategradient method.
 50. The method according to claim 47, wherein blockingprobabilities for said traffic classes are calculated based on a steadystate distribution resulting from said iterative determination.